The ratio of cups of sugar to gallons of lemonade is 3 cups to 1 gallon. How many cups of sugar are needed to make
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Answer:
Step-by-step explanation:
Recall that we say that d | a if there exists an integer k for which a = dk. So, let d = gcd(a,b) and let x, y be integers. Let t = ax+by.
We know that so there exists integers k,m such that a = kd and b = md. Then,
. Recall that since k, x, m, y are integers, then (kx+my) is also an integer. This proves that d | t.